# Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties

@article{AriasdeReyna2013CompatibleSO,
title={Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties},
author={Sara Arias-de-Reyna and Luis V. Dieulefait and Sug Woo Shin and Gabor Wiese},
journal={Mathematische Annalen},
year={2013},
volume={361},
pages={909-925}
}
• Published 9 August 2013
• Mathematics
• Mathematische Annalen
This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer $$n$$n and any positive integer $$d$$d, $$\mathrm {PSp}_n(\mathbb {F}_{\ell ^d})$$PSpn(Fℓd) or $$\mathrm {PGSp}_n(\mathbb {F}_{\ell ^d})$$PGSpn(Fℓd) occurs as a Galois group over the rational…
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